Beyond Abacus

  75th blogpost - Let's grow together Background I take inspiration from mother Nature. The infallible regularity, the spirit of giving in abundance, completely free and equally to all are truly worth emulating to the best of our capabilities. It is indeed a pleasure to recall the past 75 days’ interaction with you. I have tried my best to publish the blog at sharp 8 am IST. It has also been my constant endeavour to keep a wider variety of audience in mind - the existing maths teachers, the student - teacher pursuing her B. Ed., the wanting to be teachers, young parents wishing to revise core math concepts to help their kids and save on their tuitions, a avid reader who wants to know, revise the lost touch with mathematics. Honestly speaking, this far the focus was more on being there on time. Now that there is a milestone, regularity has been established. These days I am having 1 or 2 days’ lead time. That is, my Thursday blog is ready by Tuesday. I strive to reach one week lead...

  End of chapter Algebraic expressions Background All things good or bad should come to an end. We have been discussing language maths interface, algebraic expressions, for some time now. In this 74th blogpost I wish to share a concluding sheet that will test your understanding of forming algebraic expressions from a given statement. In the sheet below, please attempt the 11 questions given under the head Translate into algebraic symbols. From tomorrow, the focus, content and approach will change…..stay tuned Dr Prakash Moghe 8085906062, 7489447223 drpnmoghe@gmail.com

  Higher order reasoning sheet  Background The entire subject of mathematics came up from reasoning and in turn developed, enriched, the reasoning abilities. Inductive Reasoning ( From particular to General. Like, to test if rice is cooked, we test just one grain and infer about the entire rice or we test someone's employability by asking a few questions. This is inductive reasoning) and Deductive reasoning ( From general to particular, like I take the register of Class XI A, take a roll call and confirm it to be the register of Class XI A, all geometric theorem proofs are examples of deductive reasoning) are two distinct reasoning logics. The worksheet today is of higher reasoning ability. Here, in an opening para, some coding instructions are given. The testee (One who is writing the test, that is you) is supposed to follow the instructions verbatim. Means putting aside common sense. For example, if the statement is All clouds are chairs - you have start from there instea...

  Applying algebraic formulae Background While it is very important to know the various algebraic formulae - expansion, factorisation of polynomials. It is equally important to be able to apply them correctly.  The worksheet posted below has large number of questions using different algebraic expressions. On the right top, I fondly recall my three different landline numbers written. That time, late 1990s and early 2000, mobile phones were unheard of even in the higher class. Just passing by info, in the initial phase, mobile incoming rates too were around Rupees 16-17/- per minute. Even the elites used to prefer missed calls or used to use  a popular instrument called pager. Should I post answers too ? Please let me know. Also, any topic you want me to take up you can suggest here on the given numbers / mail address. Dr Prakash Moghe 8085906062, 7489447223 drpnmoghe@gmail.com

  Testing formulae knowledge Background As a mathematics teacher we have to teach different formulae in different topics. Here is a sheet I prepared that helps in a cumulative overview of many topics.  Very useful for the final revision round in standard 10th where practically all these formulae come handy in solving sums. I have designed a match the column worksheet in which each of the quantity on the left has to be matched with one unique answer on the right. Dr Prakash Moghe 8085906062, 7489447223 drpnmoghe@gmail.com

  Practicing language maths interface Answers to the worksheet Mathematical statements to equations As Final practice sheet  These are old sheets I created and used in different classes in early 2000s Dr Prakash Moghe 8085906062, 7489447223 drpnmoghe@gmail.com

  The language maths interface - 2 Background In continuity of our developing understanding of the importance of The language maths interface - 1 , today we will see an actual, entire worksheet in which statements are written and we need to form a corresponding mathematical statement for each of them.  e.g. a added to b gives c can be written mathematically as a + b  = c. When we are writing equivalent mathematical statements to a given situation, in a way we are doing mathematical modelling. Population clock, weather prediction, share market trend studies, car demand supply etc all are some of the examples where we develop mathematical models to predict the requirements. Deep understanding of the language maths interface helps a lot in this pursuit. Here are some statements for you to try your core mathematical modelling skills  Answers to the sheet will be provided tomorrow. 7 or more correct, if you are not a middle school or higher class maths teacher will mean ...

  The language maths interface - 1 Background If you ask me to list two most underrated, neglected, aspects of entire K - 12 mathematics education, even in deep sleep I would say  Geometry Language maths interface Between them too, the second is more neglected. I really don't know from where this misconception entered into the education system that language and maths are two opposite fields of knowledge and that they are exclusive. You can either be good at maths or language. As a corollary, students keep a safe distance from the statement sums which in any case are towards the end of the chapter.  After teaching for over three decades, I am convinced that a strong language foundation is necessary for being good at maths. Although maths has its own language, grammar, syntax, but beyond executing  simple four operations of addition, subtraction, multiplication and division, we need language sense to understand what is being discussed in the sum. Unfortunately, in the...

  Exterior angle property of a triangle Background As shared in 300+ maths worksheets , the objective behind writing these notes, sharing these past worksheets handmade by me, in early 2000, is to revise core maths concepts - especially for the young mothers wanting to revise their maths basics. In that series, which is not in any pedagogical sequence, today we will explore the exterior angle property of triangles. Exterior means outside the boundary. We have an external affairs ministry to handle matters outside the national boundaries. We use exterior paint for protecting the outer surface of our homes.  Same way, the exterior angle of a triangle is an angle formed outside the triangle but between an extended side and another regular side. Some students misunderstand the concept and even treat the intersection of two sides forming an exterior angle. Which, in fact, is an interior and angle.  Please note that in each of the figures shown in the sheet, the exterior angle ...

Sheet on Parallel lines  Background        As discussed in 300+ quality maths worksheets , today I am sharing a sheet I prepared as a practice  sheet on Parallel lines. Parallel means do not meet. We have parallel lines, as on your notebooks, the printed lines in a newspaper, railway tracks, healthy pair of eye balls move in parallel…motivate the students to see parallel lines in their environment; they see bars on a window, frames of the door and so on.  Then we have parallel planes. Floors in a multi storied building, opposite walls in a room, the roof and the floor. You may even trigger creativity by throwing a question for brainstorming - what would happen if the roof and floor are non parallel ?  Then we have thoughts, stories going in parallel. To illustrate our point we give parallel from life. A very popular misuse of the word parallel is saying parallaly whereas the correct usage is in parallel.  I always tried to see laterally and c...

  300+ quality Maths worksheets for you  Background I have a dream. To help young (Perhaps every reader must be younger to me, @61 😄) teachers, wanting to be maths teachers and above all Parents wanting to teach their kids to revise, learn, understand, core mathematical concepts till standard 10th. I also want my long research based knowledge, exposure, experience in mathematics education to get applied in better quality of mathematics teaching - learning.  In this pursuit, I want to detail the 12 cells of mathematics through explaining for each cell, the relevant Concepts Operations and Problem solving  What to expect ? In this long professional journey, I have worked with different international, national, boards, professionals. You can expect each sheet being presented to have some unique feature (s) that you might not have come across in that topic. Specifically, I guarantee very good quality, thought provoking sheets covering geometry content, reasoning abili...

About Divergent thinking Divergent means different, non routine, away from the normal. We use the phrase diverse views to express something non traditional or different from the normal In his epic work Guilford Model of Structure of Intellect, J. P. Guilford used the term divergent operation to represent a higher level of thinking skills as can be seen in the figure below  Let's understand it through some examples - Cognition is the ability to recognise, identify, something / someone correctly. Among the operations that our intellect does, recognising a symbol, person, touch, smell is considered as the bare minimum quality to be called an intelligent person. A child recalls alphabets, numerals, identified his mother among many other family ladies.  Memory is the next level of intelligence in terms of operations. Memory is the ability to retain what has been seen, learnt, taught etc. In the formal education and examination system, memory is too much tested. Most questions are b...

  Why are 12 cells important ?    In one of my posts, I discussed the breakthrough concepts of dividing the entire 1 to 10th maths content into 12 cells the 12 cell concept . Let's now see what are advantages in treating the school maths content like this over the traditional ways. Skill based syllabus Changing the entire content from pure academic to its being skill based makes a powerful shift of emphasis in terms of making the teaching - learning more applied and related to life. The early introduction of reasoning will give structural scope to open different higher facets of intelligence like visualisation, imagination, critical thinking, computational thinking, developing problem solving skills. The biggest advantage of breaking the syllabus into skill sets will be to end the stereotypes of relating syllabus with age and grade. Once the skill based content, evaluation, teaching stuff is ready, a 50 year old can go for learning elementary algebra, a competition aspir...